I've used BA car hire on many occasions. The combination of easy booking, reasonably competitive price, free extra driver and a few avios for the booking make it hassle free.

I've never had any issue with Avis other than lengthy queues on a couple if occasions, one of which they reimbursed a days rental for after a complaint. On one occasion on a trip to DC when I forgot to bring my drivers license, they couldn't have been more helpful in cancelling and rebooking in my wife's name whilst I waited in the Avis office.